1. Field of the Invention
The present disclosure relates to signal processing in general, and to reconstruction of distorted signals from discrete samples, in particular.
2. Description of Related Art
Digital signal processing applications are often concerned with the ability to store and process discrete sets of numbers, which are related to continuous-time signals through an acquisition process. While an analog continuous-time signal may be required by an application, only its discrete samples are often provided and processed by modern digital signal processing equipment.
In the art of digital signal processing, an analog signal is sampled by an analog-to-digital converter (ADC), such as sigma-delta ADC, pipeline ADC and the like, thus acquiring a discrete set of values of the signal at various times. The sampling process is also referred to as digitizing the analog signal. In some cases, it is desired to compute the original analog signal, or even reproduce it using a digital-to-analog converter (DAC). In several scenarios it may be desired to perform a calculation of some sort based on the original analog signal, and to that end, a determination of the original analog signal is required. In some setups, the original analog signal may be computed mathematically using its samples. In some cases, an original analog signal may be approximated by a bandlimited signal to allow for computation of the original analog signal.
In many scenarios, the ADC obtains samples of a distorted version of the original signal. The distortion may be caused by various factors, such as a sensor or an ADC itself. The distortion may be linear or nonlinear, as is known in the art. The distortion may further be memoryless or dynamic, as is known in the art. For example, in the field of digital image processing, CCD image sensors introduce memoryless, nonlinear distortions when excessive light intensity causes saturation. A phase distortion is an exemplary linear distortion caused by a phase shift introduced by a sensor.
The distortion may be introduced intentionally, for example in order to increase the possible dynamic range of the signal while avoiding amplitude clipping, or damage to the ADC.
When such distortions are introduced before the original signal is sampled, current state of the art techniques may not be able to compute the original signal, as desired.
Non-ideal samplers, such as samplers that contain low-pass filters, as are known in the art, introduce an additional setback. In case a distortion is introduced and a non-ideal sampler is utilized to obtain samples of the distorted signal, a method of computing the original signal is not known.
In view of the foregoing, there is a need for an apparatus and method capable of reconstructing an original analog signal based on a set of sampled values of a distorted version obtained by a non-ideal sampler.